Numbers Puzzle

Find all solutions to $\sqrt{PASSION} = MISS$ where alphabets stand for distinct digits from 0 to 9.

I 've got an answer by reducing thousands of possibilities to some fifty to hundred and then trial n error. Looking for precise logical arguments leading to solution. Plz help.

#Numbers #SquareRoot #PerfectSquare #Puzzle

Easy Math Editor

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Math	Appears as
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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

EDIT

I am sorry About Previous Post,I got the following pairs upon revision

0000 0000000
1000 1000000
2000 4000000
3000 9000000
2033 4133089
1312 1721344

The following prints all possible $MISS,PASSION$ pairs

print 'MISS','PASSION'
Squares = set([i**2 for i in range(10**5)])
for miss in range(0,10000):
    MISS = str(miss)
    if miss < 1000:
        MISS = '0'*(4-len(MISS))+MISS
    PASSION = str(miss**2)
    if len(PASSION)>7:continue
    else:PASSION = '0'*(7-len(PASSION))+PASSION
    if PASSION[2:5] == MISS[1:][::-1] and len(PASSION)==7:
            print MISS,PASSION

Thaddeus Abiy - 7 years, 4 months ago

hey thanks for ur attempt. But there is/are non-trivial solution(s), where each alphabet stands for different digit.

Piyushkumar Palan - 7 years, 4 months ago

Sorry,Look at my re-edited solution above

Thaddeus Abiy - 7 years, 4 months ago

@Thaddeus Abiy – yes MISS = 2033 is the only correct solution.

Piyushkumar Palan - 7 years, 4 months ago

@Piyushkumar Palan – hi piyush, i did the same way. but had to use machine (spreadsheet) for shortlisting 6 possibilities. without machine, i could reach up to m=1,2,3 and s=2,3,4,7,9. please let me know if u found the answer without using machine (calculator or computer).

Abhijit Gokhale - 6 years, 5 months ago

Finally got it.

A long sequence of logical mathematical arguments n Possibilities of MISS reduced to just 6. Then squared all six and only one matches with form of PASSION.

MISS = 2033 is the only solution.

Piyushkumar Palan - 7 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$